To improve fuel economy, vehicles are recently being provided with, for example, an idle reduction function that stops idling when the vehicle is waiting at a traffic signal or the like, a function for charging a secondary battery with regenerative power obtained by increasing the voltage generated by an alternator while decelerating, and the like. To use these functions effectively, it is necessary to accurately detect a state of the secondary battery, and determine whether or not to enable the idle reduction function, adjust the generated voltage, and the like on the basis of the detected state. The technique disclosed in Patent Document 1 can be given as an example of a conventional technique for detecting the state of a secondary battery. According to the technique disclosed in Patent Document 1, a voltage and a current of the secondary battery are measured, the measured voltage value and current value are converted into a frequency domain through a Fourier transformation, and a complex impedance is found. An equivalent circuit is then found from the obtained complex impedance, and the state of the secondary battery is detected on the basis of the equivalent circuit.